Semilinear metric semilattices on $\mathbb R$-trees
| dc.creator | Andreev, P. D. | |
| dc.date | 2005-10-17 | |
| dc.date | 2009-02-19 | |
| dc.date.accessioned | 2026-07-07T12:43:39Z | |
| dc.date.available | 2026-07-07T12:43:39Z | |
| dc.description | We introduce the notion of metric semilattice on the metric space and prove the criterion of $\R$-tree as connected geodesic metric space $X$ admitting the partial order, such that $X$ is semilinear metric semilattice. Also we state the homeomorphism between topological space of orders defining upper semilinear metric $\vee$-semilattices on locally compact complete $\mathbb R$-tree $X$ and its metric compactification $\bar{X}_m$. As an application we construct the example of locally complete non-homogeneous similarity-homogeneous space showing essentiality of the condition of locally compactness in V.N. Berestovski\vı's conjecture on the structure of such spaces. Constructed metric space is $\mathbb R$-tree, where every point is a branching point. It is the metric fibration but is not topological product with factor $\mathbb R$ and does not satisfy the Berestovski\vı's conjecture. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510344 | |
| dc.identifier | http://arxiv.org/abs/math/0510344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220497 | |
| dc.subject | Metric Geometry | |
| dc.subject | 54E50 | |
| dc.title | Semilinear metric semilattices on $\mathbb R$-trees | |
| dc.type | text |